document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=7132>Question 7132</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A container is filled with 56 litres of pine juice.  8 litres of pine juice are extracted and the container is refilled with mango juice.  The content of the container is thoroughly mixed and 8 litres are then extracted and the container is again refilled with mango juice.  What is the ratio of mango juice to pine juice in the final mixture? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #3976 by </B><A HREF=/tutors/aboutme.mpl?userid=prince_abubu><B>prince_abubu(198)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=prince_abubu><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=3976\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We start with 56 litres of pure pine juice. If they take out 8 litres, you'd then have 48 litres left. The mixture is still pure.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If it's refilled with 8 litres of mango juice, the resulting mixture will be 8 parts mango and 48 parts pine, or 1 part mango, 6 parts pine. (AKA, roughly 16.67% mango juice).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now, if they take out 8 litres from that mixture, that 8 litres will also be 1 part mango and 6 parts pine, leaving you with 48 litres of 1 part mango, 6 parts pine.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Hang on, because it gets tricky from here. We're going to use a formula here:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+q%5B1%5Dp%5B1%5D+%2B+q%5B2%5Dp%5B2%5D+=+%28q%5B1%5D%2Bq%5B2%5D%29p%5B3%5D+ ALIGN=MIDDLE  ALT=\"+q%5B1%5Dp%5B1%5D+%2B+q%5B2%5Dp%5B2%5D+=+%28q%5B1%5D%2Bq%5B2%5D%29p%5B3%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---- where there are q[1] litres of p[1] % that we start with, and we add q[2] litres of p[2] % mix, and so we'll end up with a mixture that is (q[1] + q[2]) liters big that will have a different percent mixture p[3] from what we started.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We started with 48 liters that is 16.67% mango. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+q%5B1%5D%2Ap%5B1%5D+=+48%2A0.1667+ ALIGN=MIDDLE  ALT=\"+q%5B1%5D%2Ap%5B1%5D+=+48%2A0.1667+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---- change the percent to a decimal.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We're going to add 8 liters of pure mango juice, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+q%5B2%5D%2Ap%5B2%5D+=+8%2A1+ ALIGN=MIDDLE  ALT=\"+q%5B2%5D%2Ap%5B2%5D+=+8%2A1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--- The 100% mango juice is the 1 in decimal.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "As total mix, we'll have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+q%5B1%5D%2B+q%5B2%5D+ ALIGN=MIDDLE  ALT=\"+q%5B1%5D%2B+q%5B2%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > litres which is 48 + 8 = 56, BUT the percentage mango of the new mixture will surely be different.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So our equation so far is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+48%2A0.1667+%2B+8%2A1+=+56%2Ap%5B3%5D+ ALIGN=MIDDLE  ALT=\"+48%2A0.1667+%2B+8%2A1+=+56%2Ap%5B3%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" >. All we have to do is solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5B3%5D ALIGN=MIDDLE  ALT=\"p%5B3%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++16+=+56p%5B3%5D+ ALIGN=MIDDLE  ALT=\"++16+=+56p%5B3%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---- simplified\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p%5B3%5D+=+0.2857142857+ ALIGN=MIDDLE  ALT=\"+p%5B3%5D+=+0.2857142857+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--- roughly 28.57% mango juice or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2F7+ ALIGN=MIDDLE  ALT=\"+2%2F7+\"   DISABLED_style= \"max-width:90%; height:auto;\" > mango juice. Since mango is 2/7 of the mixture, the other 5/7 is pine. The problem asked for the ratio between mango to pine, and that would be the 2:5. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );